Non-linear sphere tracing for rendering deformed signed distance fields
Non-linear sphere tracing for rendering deformed signed distance fields
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DOI：
10.1145/3355089.3356502
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发表时间：
2019-11
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影响因子：
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通讯作者：
Dario Seyb;Alec Jacobson;D. Nowrouzezahrai;Wojciech Jarosz
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文献类型：
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作者：
Dario Seyb;Alec Jacobson;D. Nowrouzezahrai;Wojciech Jarosz
符号距离场（sdf）是建模固体、体积和表面的一种强大的隐式表示。其无限的分辨率，可控的连续性和强大的建设性固体几何操作，再加上平滑的混合，使强大和直观的雕刻工具，创建复杂的SDF模型。SDF度量属性也允许使用球面跟踪进行有效的表面渲染。不幸的是，sdf仍然与许多流行的直接变形技术不兼容，这些技术通过显式表示重新定位表面。线性混合蒙皮用于字符衔接，例如，直接置换三角形网格的每个顶点。为了克服这一限制，我们提出了一种球体跟踪的变体，用于直接绘制变形的sdf。我们证明这个问题可以简化为一个非线性常微分方程的积分。我们提出了一种有效的数值解，在误差可控的情况下，首先沿着每条投射光线自动计算一个初始值，然后在未变形空间中按照带符号的距离保守地沿着弯曲光线行走。重要的是，我们的方法不需要知识，计算甚至逆变形的全局存在，这使我们能够很容易地应用许多现有的正演变形。我们展示了我们的方法对各种流行的变形技术的交互式渲染的有效性，这些技术迄今为止仅限于显式表面。
Signed distance fields (SDFs) are a powerful implicit representation for modeling solids, volumes and surfaces. Their infinite resolution, controllable continuity and robust constructive solid geometry operations, coupled with smooth blending, enable powerful and intuitive sculpting tools for creating complex SDF models. SDF metric properties also admit efficient surface rendering with sphere tracing. Unfortunately, SDFs remain incompatible with many popular direct deformation techniques which re-position a surface via its explicit representation. Linear blend skinning used in character articulation, for example, directly displaces each vertex of a triangle mesh. To overcome this limitation, we propose a variant of sphere tracing for directly rendering deformed SDFs. We show that this problem reduces to integrating a non-linear ordinary differential equation. We propose an efficient numerical solution, with controllable error, which first automatically computes an initial value along each cast ray before walking conservatively along a curved ray in the undeformed space according to the signed distance. Importantly, our approach does not require knowledge, computation or even global existence of the inverse deformation, which allows us to readily apply many existing forward deformations. We demonstrate our method's effectiveness for interactive rendering of a variety of popular deformation techniques that were, to date, limited to explicit surfaces.